arc ab is $\frac{1}{6}$ of the circumference of a circle. what is the radian measure of the central…

arc ab is $\frac{1}{6}$ of the circumference of a circle. what is the radian measure of the central angle?\n$\frac{pi}{6}$\n$\frac{pi}{3}$\n$\frac{2pi}{3}$\n$\frac{5pi}{6}$

arc ab is $\frac{1}{6}$ of the circumference of a circle. what is the radian measure of the central angle?\n$\frac{pi}{6}$\n$\frac{pi}{3}$\n$\frac{2pi}{3}$\n$\frac{5pi}{6}$

Answer

Explanation:

Step1: Recall the relationship between arc - length, circumference and central - angle

The measure of a full - circle in radians is (2\pi). If an arc is a fraction of the circumference of a circle, the radian measure of the central angle corresponding to that arc is the same fraction of (2\pi).

Step2: Calculate the radian measure of the central angle

The arc (AB) is (\frac{1}{6}) of the circumference. So the radian measure of the central angle (\theta) is (\theta=\frac{1}{6}\times2\pi). [ \begin{align*} \theta&=\frac{1}{6}\times2\pi\ &=\frac{\pi}{3} \end{align*} ]

Answer:

B. (\frac{\pi}{3})